Geometry-based material without UV or vertex paint
You are asking for an approach which avoids manually unwrapping/vertex painting, maybe the end result is more important than how you get there. For this spherical shape trigonometry offers a solution.

Nodes Approach



This approach uses the spherical property of the object. There's a relationship between the point's normal and it's normalized position: when the point normal faces outward it's closer to the normalized position of that point.





Replacing the Diffuse shader Node with a Translucent shader in this .blend also gives interesting results.